" However, considering that many "newbies" to MA consider a black belt "a master/expert", it's truly a fair enough question: how long will it take me to master this art?"

I think there are two basic false assumptions here that lead people to get frustrated by the question (and people ask it a LOT). Anyone who's spent any time in any martial art will usually realize pretty quickly that this is an entirely false assumption (first degree black belt = expert). And secondly, they will also realize that it's a pretty arbitrary scale and anyone giving out belts gets to decide for themselves what level it means (and there are very wide ranging opinions on what's optimal or what it 'should' mean), so there's no reason it can't mean entirely different things in different martial arts/dojos/organizations/countries, which it does.

BTW the literal translation of 'shodan' (aka first degree black belt) is something like 'first step', i.e., it was originally a beginner rank, and generally still is in most arts that I'm aware of, though there's often debate about precisely how beginner it should be (is it enough to not trip over your own feet anymore or should it mean you've got the basics in place or should you be able to start a dojo under supervision, etc). Consider also that many martial arts have sometimes as much as ten different 'black belt' ranks, so the first one often comes pretty early on.

As far as difference in time and intensity of training, of course that makes a difference too, and is another reason why asking people how long they've trained is not usually that helpful (and yet another reason why 'how long does it take to get a black belt' is not easily or meaningfully answerable). But it's also equally common that giving a rank more quickly primarily means that they give it earlier (at a lower 'objective' level), which is perfectly fine, but tends to make it relatively meaningless to use it as any kind of standard or comparison, particularly between different organizations or different martial arts.

I.e., martial arts have very very very little in common with universities.